The COVID-19 pandemic has caused a lot of stress for healthcare personnel. They are subjected to arduous and stressful working hours and may contract infection. The objectives of this study were to (i) assess the level of occupational stress and the prevalence of burnout among healthcare workers (HCWs) in the Kingdom of Saudi Arabia during the COVID-19 pandemic and (ii) to identify some sociodemographic characteristics and work-related factors that may influence the level of stress and burnout among such HCWs. An online survey was distributed on social media websites and groups of HCWs in KSA. The survey depended on the stress domain of Depression, Anxiety, and Stress Scale-21 (DASS-21) and the work related burnout domain of the Copenhagen Burnout Inventory (CBI). Data were collected using a Google form and then analyzed. Among 478 respondents, 37.7% of studied HCWs reported mild to extremely severe stress, and 47.9% of them reported work-related burnout. Occupational stress and burnout were more prevalent among front-line HCWs (43.9% and 55%) than among second-line HCWs (31.2% and 40.8%). The mean scores of occupational stress and burnout were significantly much higher among frontline physicians and nurses, particularly those who are females, of younger age (≤40 years), with few years of work experience (≤15 years), being married, having chronic disease, and those previously infected by COVID-19. HCWs reported a high prevalence of occupational stress and burnout during the COVID-19 pandemic. Establishing policies and guidelines, enhancing working conditions, and providing continuous psychological support and assurance to HCWs are recommended to improve their resilience and increase their coping capacities toward pandemics.